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In a tetrahedron, all three pairs of opposite (skew) edges are mutually perpendicular. Prove that the midpoints of the six edges of the tetrahedron lie on one sphere.

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#NaslovOznakeRj.KvalitetaTežina
1979IMO Shortlist 1997 problem 230
1650IMO Shortlist 1985 problem 90
1559IMO Shortlist 1981 problem 20
1455IMO Shortlist 1973 problem 130
1443IMO Shortlist 1973 problem 10
1277IMO Shortlist 1967 problem 20